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NAME

       ZSYMM  - perform one of the matrix-matrix operations   C := alpha*A*B +
       beta*C,

SYNOPSIS

       SUBROUTINE ZSYMM ( SIDE, UPLO, M, N, ALPHA, A, LDA, B,  LDB,  BETA,  C,
                        LDC )

           CHARACTER*1  SIDE, UPLO

           INTEGER      M, N, LDA, LDB, LDC

           COMPLEX*16   ALPHA, BETA

           COMPLEX*16   A( LDA, * ), B( LDB, * ), C( LDC, * )

PURPOSE

       ZSYMM  performs one of the matrix-matrix operations

       or

          C := alpha*B*A + beta*C,

       where  alpha and beta are scalars, A is a symmetric matrix and  B and C
       are m by n matrices.

PARAMETERS

       SIDE   - CHARACTER*1.
              On entry,  SIDE  specifies whether   the   symmetric  matrix   A
              appears on the  left or right  in the  operation as follows:

              SIDE = ’L’ or ’l’   C := alpha*A*B + beta*C,

              SIDE = ’R’ or ’r’   C := alpha*B*A + beta*C,

              Unchanged on exit.

       UPLO   - CHARACTER*1.
              On   entry,    UPLO   specifies   whether  the  upper  or  lower
              triangular  part  of  the  symmetric  matrix    A   is   to   be
              referenced as follows:

              UPLO  =  ’U’  or  ’u’    Only  the  upper triangular part of the
              symmetric matrix is to be referenced.

              UPLO = ’L’ or ’l’    Only  the  lower  triangular  part  of  the
              symmetric matrix is to be referenced.

              Unchanged on exit.

       M      - INTEGER.
              On  entry,  M  specifies the number of rows of the matrix  C.  M
              must be at least zero.  Unchanged on exit.

       N      - INTEGER.
              On entry, N specifies the number of columns of the matrix C.   N
              must be at least zero.  Unchanged on exit.

       ALPHA  - COMPLEX*16      .
              On  entry, ALPHA specifies the scalar alpha.  Unchanged on exit.

       A      - COMPLEX*16       array of DIMENSION ( LDA, ka ), where ka is
              m  when  SIDE = ’L’ or ’l’  and is n  otherwise.   Before  entry
              with   SIDE  =  ’L’  or  ’l’,  the  m by m  part of the array  A
              must contain the  symmetric matrix,  such that when  UPLO =  ’U’
              or ’u’, the leading m by m upper triangular part of the array  A
              must contain the upper triangular part of the  symmetric  matrix
              and   the   strictly   lower  triangular  part  of   A   is  not
              referenced,  and when  UPLO = ’L’ or ’l’, the leading   m  by  m
              lower  triangular  part   of  the   array   A must  contain  the
              lower  triangular  part   of  the   symmetric  matrix  and   the
              strictly upper triangular part of  A  is not referenced.  Before
              entry  with  SIDE = ’R’ or ’r’,  the  n by n  part of the  array
              A   must  contain the  symmetric matrix,  such that when  UPLO =
              ’U’ or ’u’, the leading n by n  upper  triangular  part  of  the
              array   A   must  contain  the  upper  triangular  part  of  the
              symmetric matrix and the  strictly  lower triangular part of   A
              is  not referenced,  and when  UPLO = ’L’ or ’l’, the leading  n
              by n  lower triangular part  of the  array  A must  contain  the
              lower   triangular  part   of  the   symmetric  matrix  and  the
              strictly  upper  triangular  part  of   A   is  not  referenced.
              Unchanged on exit.

       LDA    - INTEGER.
              On  entry, LDA specifies the first dimension of A as declared in
              the  calling (sub) program. When  SIDE = ’L’ or  ’l’   then  LDA
              must  be  at least  max( 1, m ), otherwise  LDA must be at least
              max( 1, n ).  Unchanged on exit.

       B      - COMPLEX*16       array of DIMENSION ( LDB, n ).
              Before entry, the leading  m by n part of  the  array   B   must
              contain the matrix B.  Unchanged on exit.

       LDB    - INTEGER.
              On  entry, LDB specifies the first dimension of B as declared in
              the  calling  (sub)  program.   LDB  must  be  at  least max( 1,
              m ).  Unchanged on exit.

       BETA   - COMPLEX*16      .
              On  entry,   BETA   specifies  the scalar  beta.  When  BETA  is
              supplied as zero then C need not be set on input.  Unchanged  on
              exit.

       C      - COMPLEX*16       array of DIMENSION ( LDC, n ).
              Before  entry,  the  leading   m by n  part of the array  C must
              contain the matrix  C,  except when  beta   is  zero,  in  which
              case  C  need  not  be  set on entry.  On exit, the array  C  is
              overwritten by the  m by n updated matrix.

       LDC    - INTEGER.
              On entry, LDC specifies the first dimension of C as declared  in
              the  calling  (sub)  program.   LDC  must  be  at  least max( 1,
              m ).  Unchanged on exit.

              Level 3 Blas routine.

              -- Written on 8-February-1989.  Jack Dongarra, Argonne  National
              Laboratory.  Iain Duff, AERE Harwell.  Jeremy Du Croz, Numerical
              Algorithms Group Ltd.   Sven  Hammarling,  Numerical  Algorithms
              Group Ltd.